formal Picard group

- group, ∞-group
- group object, group object in an (∞,1)-category
- abelian group, spectrum
- group action, ∞-action
- representation, ∞-representation
- progroup
- homogeneous space

Given an algebraic variety with Picard scheme $Pic_X$, if the connected component $Pic_X^0$ is a smooth scheme then the completion of $Pic_X$ at its neutral global point is a formal group. This is called the *formal Picard group*of $X$. (ArtinMazur 77, Liedtke 14, example 6.13)

This construction is the special case of the general construction of Artin-Mazur formal groups for $n = 1$. The next case is called the *formal Brauer group*.

**moduli spaces of line n-bundles with connection on $n$-dimensional $X$**

The original account of the construction of formal Picard groups is

- Michael Artin, Barry Mazur,
*Formal Groups Arising from Algebraic Varieties*, Annales scientifiques de l’École Normale Supérieure, Sér. 4, 10 no. 1 (1977), p. 87-131 numdam, MR56:15663

Modern reviews include

- Christian Liedtke, example 6.13 in
*Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem*(arXiv.1403.2538)

Last revised on May 21, 2014 at 21:22:39. See the history of this page for a list of all contributions to it.